A process is controlled with a fraction nonconforming control chart with three-sigma limits, n = 100, UCL = 0.161, center line = 0.080, and LCL = 0.

a. Find the equivalent control chart for the number nonconforming.
b. Use the Poisson approximation to the binomial to find the probability of a type I error.
c. Use the normal approximation to binomial to find the probability of a type II error if the process fraction nonconforming shifts to 0.2.
d. What is the probability of detecting the shift in part (c) by at most the fourth sample after the shift?

Lets Recall, p= 0.080, n=100, UCL= 0.161

Then np=100, 0.080=8

Step-by-step explanation:

The full steps or solution to this is in an an attached document.

the data of the detroit pistons in numerical order from least to greatest is 0.30, 0.37, 0.55, 0.62, 0.69, 0.72, 0.73, 0.75, 0.77, 0.78, 0.80, 0.81, 0.81, 0.83, 0.84, 0.89

the data of the miami heat in numerical order from least to greatest is 0.50, 0.50, 0.56, 0.57, 0.67, 0.72, 0.72, 0.72, 0.75, 0.75, 0.76, 0.81, 0.82, 0.90, 1.00, 1.00

the detroit pistons median : 1.52

the miami heat median: 1.47

the iqr of this data is 0.05